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A232113 a(n) is the Manhattan distance between n and 2*n in a square spiral of positive integers with 1 at the center. 4
1, 2, 3, 2, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10, 11, 8, 11, 12, 13, 12, 9, 10, 13, 16, 15, 12, 9, 12, 15, 16, 15, 12, 9, 12, 15, 14, 13, 12, 11, 12, 13, 12, 11, 10, 9, 10, 11, 10, 9, 8, 7, 8, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Spiral begins:

.

  49  26--27--28--29--30--31

   |   |                   |

  48  25  10--11--12--13  32

   |   |   |           |   |

  47  24   9   2---3  14  33

   |   |   |   |   |   |   |

  46  23   8   1   4  15  34

   |   |   |       |   |   |

  45  22   7---6---5  16  35

   |   |               |   |

  44  21--20--19--18--17  36

   |                       |

  43--42--41--40--39--38--37

.

Numbers n such that a(n)^2=n: 1, 4, 16, 625, 20736, 707281, 24010000, 815730721, ...; that is, 1, 4, 2^4, 5^4, 12^4, 29^4, 70^4, 169^4, ... (cf. Pell numbers: A000129).

LINKS

Table of n, a(n) for n=1..79.

CROSSREFS

Cf. A000129, A214526, A232114, A232115.

Sequence in context: A278327 A067316 A210221 * A216475 A267807 A127433

Adjacent sequences:  A232110 A232111 A232112 * A232114 A232115 A232116

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Nov 19 2013

STATUS

approved

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Last modified September 25 16:53 EDT 2022. Contains 356986 sequences. (Running on oeis4.)